Question: Between which two consecutive whole numbers does $\sqrt{59}$ lie? Fill out the sentence below to justify your answer and use your mouse to drag $\sqrt{59}$ to an approximately correct location on the number line.
$\sqrt{59}$
Real
Answer
Attempt 1 out of 2
Since $\sqrt{\square} = \square$ and $\sqrt{\square} = \square$ it is known that $\sqrt{59}$ is between $\square$
and $\square$.
Submit Answer
Graph: a horizontal number line labeled Real, with integer marks from 0 to 10; the point label $\sqrt{59}$ is positioned above the line between 7 and 8, slightly closer to 8. position_hint: center
1. **State the problem:** We need to find between which two consecutive whole numbers the value of $\sqrt{59}$ lies.
2. **Recall the perfect squares near 59:**
- $7^2 = 49$
- $8^2 = 64$
3. **Compare 59 with these perfect squares:**
Since $49 < 59 < 64$, it follows that
$$\sqrt{49} < \sqrt{59} < \sqrt{64}$$
which means
$$7 < \sqrt{59} < 8$$
4. **Fill in the sentence:**
Since $\sqrt{49} = 7$ and $\sqrt{64} = 8$ it is known that $\sqrt{59}$ is between $7$ and $8$.
5. **Approximate location on the number line:**
$\sqrt{59}$ is closer to $8$ than to $7$ because $59$ is closer to $64$ than to $49$.
**Final answer:** $\sqrt{59}$ lies between the consecutive whole numbers $7$ and $8$.